// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#include "main.h"
#include <Eigen/Geometry>
#include <Eigen/LU>
#include <Eigen/QR>

template<typename HyperplaneType>
void
hyperplane(const HyperplaneType& _plane)
{
	/* this test covers the following files:
	   Hyperplane.h
	*/
	using std::abs;
	const Index dim = _plane.dim();
	enum
	{
		Options = HyperplaneType::Options
	};
	typedef typename HyperplaneType::Scalar Scalar;
	typedef typename HyperplaneType::RealScalar RealScalar;
	typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime, 1> VectorType;
	typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime, HyperplaneType::AmbientDimAtCompileTime> MatrixType;

	VectorType p0 = VectorType::Random(dim);
	VectorType p1 = VectorType::Random(dim);

	VectorType n0 = VectorType::Random(dim).normalized();
	VectorType n1 = VectorType::Random(dim).normalized();

	HyperplaneType pl0(n0, p0);
	HyperplaneType pl1(n1, p1);
	HyperplaneType pl2 = pl1;

	Scalar s0 = internal::random<Scalar>();
	Scalar s1 = internal::random<Scalar>();

	VERIFY_IS_APPROX(n1.dot(n1), Scalar(1));

	VERIFY_IS_MUCH_SMALLER_THAN(pl0.absDistance(p0), Scalar(1));
	if (numext::abs2(s0) > RealScalar(1e-6))
		VERIFY_IS_APPROX(pl1.signedDistance(p1 + n1 * s0), s0);
	else
		VERIFY_IS_MUCH_SMALLER_THAN(abs(pl1.signedDistance(p1 + n1 * s0) - s0), Scalar(1));
	VERIFY_IS_MUCH_SMALLER_THAN(pl1.signedDistance(pl1.projection(p0)), Scalar(1));
	VERIFY_IS_MUCH_SMALLER_THAN(pl1.absDistance(p1 + pl1.normal().unitOrthogonal() * s1), Scalar(1));

	// transform
	if (!NumTraits<Scalar>::IsComplex) {
		MatrixType rot = MatrixType::Random(dim, dim).householderQr().householderQ();
		DiagonalMatrix<Scalar, HyperplaneType::AmbientDimAtCompileTime> scaling(VectorType::Random());
		Translation<Scalar, HyperplaneType::AmbientDimAtCompileTime> translation(VectorType::Random());

		while (scaling.diagonal().cwiseAbs().minCoeff() < RealScalar(1e-4))
			scaling.diagonal() = VectorType::Random();

		pl2 = pl1;
		VERIFY_IS_MUCH_SMALLER_THAN(pl2.transform(rot).absDistance(rot * p1), Scalar(1));
		pl2 = pl1;
		VERIFY_IS_MUCH_SMALLER_THAN(pl2.transform(rot, Isometry).absDistance(rot * p1), Scalar(1));
		pl2 = pl1;
		VERIFY_IS_MUCH_SMALLER_THAN(pl2.transform(rot * scaling).absDistance((rot * scaling) * p1), Scalar(1));
		VERIFY_IS_APPROX(pl2.normal().norm(), RealScalar(1));
		pl2 = pl1;
		VERIFY_IS_MUCH_SMALLER_THAN(
			pl2.transform(rot * scaling * translation).absDistance((rot * scaling * translation) * p1), Scalar(1));
		VERIFY_IS_APPROX(pl2.normal().norm(), RealScalar(1));
		pl2 = pl1;
		VERIFY_IS_MUCH_SMALLER_THAN(pl2.transform(rot * translation, Isometry).absDistance((rot * translation) * p1),
									Scalar(1));
		VERIFY_IS_APPROX(pl2.normal().norm(), RealScalar(1));
	}

	// casting
	const int Dim = HyperplaneType::AmbientDimAtCompileTime;
	typedef typename GetDifferentType<Scalar>::type OtherScalar;
	Hyperplane<OtherScalar, Dim, Options> hp1f = pl1.template cast<OtherScalar>();
	VERIFY_IS_APPROX(hp1f.template cast<Scalar>(), pl1);
	Hyperplane<Scalar, Dim, Options> hp1d = pl1.template cast<Scalar>();
	VERIFY_IS_APPROX(hp1d.template cast<Scalar>(), pl1);
}

template<typename Scalar>
void
lines()
{
	using std::abs;
	typedef Hyperplane<Scalar, 2> HLine;
	typedef ParametrizedLine<Scalar, 2> PLine;
	typedef Matrix<Scalar, 2, 1> Vector;
	typedef Matrix<Scalar, 3, 1> CoeffsType;

	for (int i = 0; i < 10; i++) {
		Vector center = Vector::Random();
		Vector u = Vector::Random();
		Vector v = Vector::Random();
		Scalar a = internal::random<Scalar>();
		while (abs(a - 1) < Scalar(1e-4))
			a = internal::random<Scalar>();
		while (u.norm() < Scalar(1e-4))
			u = Vector::Random();
		while (v.norm() < Scalar(1e-4))
			v = Vector::Random();

		HLine line_u = HLine::Through(center + u, center + a * u);
		HLine line_v = HLine::Through(center + v, center + a * v);

		// the line equations should be normalized so that a^2+b^2=1
		VERIFY_IS_APPROX(line_u.normal().norm(), Scalar(1));
		VERIFY_IS_APPROX(line_v.normal().norm(), Scalar(1));

		Vector result = line_u.intersection(line_v);

		// the lines should intersect at the point we called "center"
		if (abs(a - 1) > Scalar(1e-2) && abs(v.normalized().dot(u.normalized())) < Scalar(0.9))
			VERIFY_IS_APPROX(result, center);

		// check conversions between two types of lines
		PLine pl(line_u); // gcc 3.3 will crash if we don't name this variable.
		HLine line_u2(pl);
		CoeffsType converted_coeffs = line_u2.coeffs();
		if (line_u2.normal().dot(line_u.normal()) < Scalar(0))
			converted_coeffs = -line_u2.coeffs();
		VERIFY(line_u.coeffs().isApprox(converted_coeffs));
	}
}

template<typename Scalar>
void
planes()
{
	using std::abs;
	typedef Hyperplane<Scalar, 3> Plane;
	typedef Matrix<Scalar, 3, 1> Vector;

	for (int i = 0; i < 10; i++) {
		Vector v0 = Vector::Random();
		Vector v1(v0), v2(v0);
		if (internal::random<double>(0, 1) > 0.25)
			v1 += Vector::Random();
		if (internal::random<double>(0, 1) > 0.25)
			v2 += v1 * std::pow(internal::random<Scalar>(0, 1), internal::random<int>(1, 16));
		if (internal::random<double>(0, 1) > 0.25)
			v2 += Vector::Random() * std::pow(internal::random<Scalar>(0, 1), internal::random<int>(1, 16));

		Plane p0 = Plane::Through(v0, v1, v2);

		VERIFY_IS_APPROX(p0.normal().norm(), Scalar(1));
		VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v0), Scalar(1));
		VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v1), Scalar(1));
		VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v2), Scalar(1));
	}
}

template<typename Scalar>
void
hyperplane_alignment()
{
	typedef Hyperplane<Scalar, 3, AutoAlign> Plane3a;
	typedef Hyperplane<Scalar, 3, DontAlign> Plane3u;

	EIGEN_ALIGN_MAX Scalar array1[4];
	EIGEN_ALIGN_MAX Scalar array2[4];
	EIGEN_ALIGN_MAX Scalar array3[4 + 1];
	Scalar* array3u = array3 + 1;

	Plane3a* p1 = ::new (reinterpret_cast<void*>(array1)) Plane3a;
	Plane3u* p2 = ::new (reinterpret_cast<void*>(array2)) Plane3u;
	Plane3u* p3 = ::new (reinterpret_cast<void*>(array3u)) Plane3u;

	p1->coeffs().setRandom();
	*p2 = *p1;
	*p3 = *p1;

	VERIFY_IS_APPROX(p1->coeffs(), p2->coeffs());
	VERIFY_IS_APPROX(p1->coeffs(), p3->coeffs());
}

EIGEN_DECLARE_TEST(geo_hyperplane)
{
	for (int i = 0; i < g_repeat; i++) {
		CALL_SUBTEST_1(hyperplane(Hyperplane<float, 2>()));
		CALL_SUBTEST_2(hyperplane(Hyperplane<float, 3>()));
		CALL_SUBTEST_2(hyperplane(Hyperplane<float, 3, DontAlign>()));
		CALL_SUBTEST_2(hyperplane_alignment<float>());
		CALL_SUBTEST_3(hyperplane(Hyperplane<double, 4>()));
		CALL_SUBTEST_4(hyperplane(Hyperplane<std::complex<double>, 5>()));
		CALL_SUBTEST_1(lines<float>());
		CALL_SUBTEST_3(lines<double>());
		CALL_SUBTEST_2(planes<float>());
		CALL_SUBTEST_5(planes<double>());
	}
}
